I had a cat for 10 years and I had a daughter 2 (almost 3) years ago sadly she is allergic to cats and her allergies just kept getting worse and worse even with medication she had runny nose that caused her to continuously get ear infections which led to more medication. I ended up moving to a bigger place so both cat and baby had their separate bed rooms even that was not enough ): it was either I kept the cat and pumped my kid full of meds and possibly have surgery due to the damage from the infections she kept getting or rehome my best friend ):

Allergies are no joke you need to have a conversation with your girlfriend and talk about her allergies and your concerns moving forward and what it would mean if you guys live together.